{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fourier analysis & resonances\n",
    "\n",
    "A great benefit of being able to call rebound from within python is the ability to directly apply sophisticated analysis tools from scipy and other python libraries.  Here we will do a simple Fourier analysis of a reduced Solar System consisting of Jupiter and Saturn.  Let's begin by setting our units and adding these planets using JPL's horizons database:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Searching NASA Horizons for 'Sun'... Found: Sun (10).\n",
      "Searching NASA Horizons for 'Jupiter'... Found: Jupiter Barycenter (5).\n",
      "Searching NASA Horizons for 'Saturn'... Found: Saturn Barycenter (6).\n"
     ]
    }
   ],
   "source": [
    "import rebound\n",
    "import numpy as np\n",
    "sim = rebound.Simulation()\n",
    "sim.units = ('AU', 'yr', 'Msun')\n",
    "sim.add(\"Sun\")\n",
    "sim.add(\"Jupiter\")\n",
    "sim.add(\"Saturn\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's set the integrator to whfast, and sacrificing accuracy for speed, set the timestep for the integration to about $10\\%$ of Jupiter's orbital period."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sim.integrator = \"whfast\"\n",
    "sim.dt = 1. # in years.  About 10% of Jupiter's period\n",
    "sim.move_to_com()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last line (moving to the center of mass frame) is important to take out the linear drift in positions due to the constant COM motion.  Without it we would erase some of the signal at low frequencies.\n",
    "\n",
    "Now let's run the integration, storing time series for the two planets' eccentricities (for plotting) and x-positions (for the Fourier analysis).  Additionally, we store the mean longitudes and pericenter longitudes (varpi) for reasons that will become clear below.  Having some idea of what the secular timescales are in the Solar System, we'll run the integration for $3\\times 10^5$ yrs.  We choose to collect $10^5$ outputs in order to resolve the planets' orbital periods ($\\sim 10$ yrs) in the Fourier spectrum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Nout = 100000\n",
    "tmax = 3.e5\n",
    "Nplanets = 2\n",
    "\n",
    "x = np.zeros((Nplanets,Nout))\n",
    "ecc = np.zeros((Nplanets,Nout))\n",
    "longitude = np.zeros((Nplanets,Nout))\n",
    "varpi = np.zeros((Nplanets,Nout))\n",
    "\n",
    "times = np.linspace(0.,tmax,Nout)\n",
    "ps = sim.particles\n",
    "\n",
    "for i,time in enumerate(times):\n",
    "    sim.integrate(time) \n",
    "    # note we used above the default exact_finish_time = 1, which changes the timestep near the outputs to match\n",
    "    # the output times we want.  This is what we want for a Fourier spectrum, but technically breaks WHFast's\n",
    "    # symplectic nature.  Not a big deal here.\n",
    "    os = sim.orbits()\n",
    "    for j in range(Nplanets):\n",
    "        x[j][i] = ps[j+1].x  # we use the 0 index in x for Jup and 1 for Sat, but the indices for ps start with the Sun at 0\n",
    "        ecc[j][i] = os[j].e\n",
    "        longitude[j][i] = os[j].l\n",
    "        varpi[j][i] = os[j].Omega + os[j].omega"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see what the eccentricity evolution looks like with matplotlib:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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gsM7RuMY76NYQHBgMGktRpUgVUfvEzRMxb+88RlFxnDHdeHBDtr11xdYIDAjU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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111690f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "labels = [\"Jupiter\", \"Saturn\"]\n",
    "import matplotlib.pyplot as plt\n",
    "fig = plt.figure(figsize=(12,5))\n",
    "ax = plt.subplot(111)\n",
    "plt.plot(times,ecc[0],label=labels[0])\n",
    "plt.plot(times,ecc[1],label=labels[1])\n",
    "ax.set_xlabel(\"Time (yrs)\")\n",
    "ax.set_ylabel(\"Eccentricity\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's try to analyze the periodicities in this signal.  Here we have a uniformly spaced time series, so we could run a Fast Fourier Transform, but as an example of the wider array of tools available through scipy, let's run a Lomb-Scargle periodogram (which allows for non-uniform time series). This could also be used when storing outputs at each timestep using the integrator IAS15 (which uses adaptive and therefore non-uniform timesteps).\n",
    "\n",
    "Let's check for periodicities with periods logarithmically spaced between 10 and $10^5$ yrs.  From the documentation, we find that the lombscargle function requires a list of corresponding angular frequencies (ws), and we obtain the appropriate normalization for the plot.  To avoid conversions to orbital elements, we analyze the time series of Jupiter's x-position."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1118f6d90>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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g2MWSevanBQAAACpqsFS8Ky1txfuQmY1QTKiUmR2jaP8AAADAIMNyguVJW/FeJOluSbPM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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f5d23d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import signal\n",
    "Npts = 3000\n",
    "logPmin = np.log10(10.)\n",
    "logPmax = np.log10(1.e5)\n",
    "Ps = np.logspace(logPmin,logPmax,Npts)\n",
    "ws = np.asarray([2*np.pi/P for P in Ps])\n",
    "\n",
    "periodogram = signal.lombscargle(times,x[0],ws)\n",
    "\n",
    "fig = plt.figure(figsize=(12,5))\n",
    "ax = plt.subplot(111)\n",
    "ax.plot(Ps,np.sqrt(4*periodogram/Nout))\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim([10**logPmin,10**logPmax])\n",
    "ax.set_ylim([0,0.15])\n",
    "ax.set_xlabel(\"Period (yrs)\")\n",
    "ax.set_ylabel(\"Power\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We pick out the obvious signal in the eccentricity plot with a period of $\\approx 45000$ yrs, which is due to secular interactions between the two planets.  There is quite a bit of power aliased into neighbouring frequencies due to the short integration duration, with contributions from the second secular timescale, which is out at $\\sim 2\\times10^5$ yrs and causes a slower, low-amplitude modulation of the eccentricity signal plotted above (we limited the time of integration so that the example runs in a few seconds).  \n",
    "\n",
    "Additionally, though it was invisible on the scale of the eccentricity plot above, we clearly see a strong signal at Jupiter's orbital period of about 12 years.  \n",
    "\n",
    "But wait!  Even on this scale set by the dominant frequencies of the problem, we see an additional blip just below $10^3$ yrs.  Such a periodicity is actually visible in the above eccentricity plot if you inspect the thickness of the lines. Let's investigate by narrowing the period range:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x111dcc790>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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i8Q/fubaOeCiaEnLEx40D3v524E9/SuYfMUL/ud+B64i70RRfiC9bphEW3zkP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\n2EoBOtApIDkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112531690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,5))\n",
    "ax = plt.subplot(111)\n",
    "ax.plot(Ps,np.sqrt(4*periodogram/Nout))\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim([600,1600])\n",
    "ax.set_ylim([0,0.003])\n",
    "ax.set_xlabel(\"Period (yrs)\")\n",
    "ax.set_ylabel(\"Power\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the right timescale to be due to resonant perturbations between giant planets ($\\sim 100$ orbits).  In fact, Jupiter and Saturn are close to a 5:2 mean-motion resonance.  This is the famous great inequality that Laplace showed was responsible for slight offsets in the predicted positions of the two giant planets.  Let's check whether this is in fact responsible for the peak.  \n",
    "\n",
    "In this case, we have that the mean longitude of Jupiter $\\lambda_J$ cycles approximately 5 times for every 2 of Saturn's ($\\lambda_S$).  The game is to construct a slowly-varying resonant angle, which here could be $\\phi_{5:2} = 5\\lambda_S - 2\\lambda_J - 3\\varpi_J$, where $\\varpi_J$ is Jupiter's longitude of pericenter.  This last term is a much smaller contribution to the variation of $\\phi_{5:2}$ than the first two, but ensures that the coefficients in the resonant angle sum to zero and therefore that the physics do not depend on your choice of coordinates.\n",
    "\n",
    "To see a clear trend, we have to shift each value of $\\phi_{5:2}$ into the range $[0,360]$ degrees, so we define a small helper function that does the wrapping and conversion to degrees:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def zeroTo360(val):\n",
    "    while val < 0:\n",
    "        val += 2*np.pi\n",
    "    while val > 2*np.pi:\n",
    "        val -= 2*np.pi\n",
    "    return val*180/np.pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we construct $\\phi_{5:2}$ and plot it over the first 5000 yrs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11131ff90>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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qWrnaKdUvTi452ctSegBvZ4+MNwHOsdZeBqwC6rqIK1XdusFBB8FTT7mORPml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\n/B+IS0vkK7xKhgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111804090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phi = [zeroTo360(5.*longitude[1][i] - 2.*longitude[0][i] - 3.*varpi[0][i]) for i in range(Nout)]\n",
    "fig = plt.figure(figsize=(12,5))\n",
    "ax = plt.subplot(111)\n",
    "ax.plot(times,phi)\n",
    "ax.set_xlim([0,5.e3])\n",
    "ax.set_ylim([0,360.])\n",
    "ax.set_xlabel(\"time (yrs)\")\n",
    "ax.set_ylabel(r\"$\\phi_{5:2}$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the resonant angle $\\phi_{5:2}$ circulates, but with a long period of $\\approx 900$ yrs (compared to the orbital periods of $\\sim 10$ yrs), which precisely matches the blip we saw in the Lomb-Scargle periodogram.  This is approximately the same oscillation period observed in the Solar System, despite our simplified setup!\n",
    "\n",
    "This resonant angle is able to have a visible effect because its (small) effects build up coherently over many orbits.   As a further illustration, other resonance angles like those at the 2:1 will circulate much faster (because Jupiter and Saturn's period ratio is not close to 2).  We can easily plot this.  Taking one of the 2:1 resonance angles $\\phi_{2:1} = 2\\lambda_S - \\lambda_J - \\varpi_J$,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10f155ad0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kNqi7oGvEh2H4OIBvn/j7XQC+e6bPtQCulcbuOYMlgIUmNehh3VuHtqbDal9L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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11131f8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phi2 = [zeroTo360(2*longitude[1][i] - longitude[0][i] - varpi[0][i]) for i in range(Nout)]\n",
    "fig = plt.figure(figsize=(12,5))\n",
    "ax = plt.subplot(111)\n",
    "ax.plot(times,phi2)\n",
    "ax.set_xlim([0,5.e3])\n",
    "ax.set_ylim([0,360.])\n",
    "ax.set_xlabel(\"time (yrs)\")\n",
    "ax.set_ylabel(r\"$\\phi_{2:1}$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "In this case, since we are far from this particular resonance (the 2:1), the corresponding resonance angles vary on fast (orbital) timescales, and their effects simply average out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
